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Radiation design in computed tomography via convex optimization

Anatoli Juditsky, Arkadi Nemirovski, Michael Zibulevsky

TL;DR

This work proposes a general convex optimization framework that takes into account patient anatomy, radiation sensitivity of different organs and tissues, and location of regions of interest to reduce effective radiation dose in computed tomography without compromising image quality.

Abstract

Proper X-ray radiation design (via dynamic fluence field modulation, FFM) allows to reduce effective radiation dose in computed tomography without compromising image quality. It takes into account patient anatomy, radiation sensitivity of different organs and tissues, and location of regions of interest. We account all these factors within a general convex optimization framework.

Radiation design in computed tomography via convex optimization

TL;DR

This work proposes a general convex optimization framework that takes into account patient anatomy, radiation sensitivity of different organs and tissues, and location of regions of interest to reduce effective radiation dose in computed tomography without compromising image quality.

Abstract

Proper X-ray radiation design (via dynamic fluence field modulation, FFM) allows to reduce effective radiation dose in computed tomography without compromising image quality. It takes into account patient anatomy, radiation sensitivity of different organs and tissues, and location of regions of interest. We account all these factors within a general convex optimization framework.
Paper Structure (16 sections, 1 theorem, 18 equations, 4 figures)

This paper contains 16 sections, 1 theorem, 18 equations, 4 figures.

Table of Contents

  1. Introduction
  2. CT Radiation Design
  3. CT observation scheme
  4. Radiation sensitivity - from voxels to bins
  5. Maximum Likelihood estimate
  6. Radiation Design via Loss index minimization
  7. Regularization
  8. Alternating minimization.
  9. Computational experiment
  10. Experimental setup
  11. Computations
  12. Numerical results
  13. Concluding remarks
  14. 3D reconstruction
  15. Radiation design under constraints
  16. ...and 1 more sections

Key Result

Proposition 1

Let $P$ be an $m\times n$ matrix of rank $n$, $B$ be a $k\times n$ matrix, and $q,\rho$ be positive $m$-dimensional vectors. Then, setting $W=W[q]:={\mathrm{Diag}}\{q_i\rho_i,i\leq m\}$, where $\|\cdot\|_F$ is the Frobenius norm

Figures (4)

  • Figure 1: Top row: phantom, sensitivity image and region of interest (ROI). Bottom row: phantom sinogram, sensitivity of the bins and sinogram of the ROI.
  • Figure 2: Radiation design for regularization $\lambda$=1e3 (right image.) For comparison, sensitivity and ROI sinograms are presented in the left and the middle plots.
  • Figure 3: Distribution of the MSE in experiments with $\lambda=0$ (left plot) and $\lambda=1$e$3$ (right plot): blue histogram---baseline design, red histogram---optimized design.
  • Figure 4: Original and reconstructed ROI (baseline and optimized designs), $\lambda=0$.

Theorems & Definitions (1)

  • Proposition 1